Group is a mathematical term commonly used in particle physics. A group is a mathematical set together with at least one operation that explains how to combine any two elements of the group to form a third element. The set and its operations must satisfy the mathematical properties of identity (there is an element that leaves other group elements unchanged when the two are combined), closure (combining any two group elements yields another element in the group), associativity (it doesn't matter in what order you perform a series of operations on a list of elements so long as the order of the list doesn't change), and invertability (every operation can be reversed by combining the result with another element in the group). For example, the set of real numbers is a group with respect to the addition operator. A symmetry group is the set of all transformations that leave a physical system in a state indistinguishable from the starting state.